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Evolution of the Euler-Maclaurin sum formula

Published online by Cambridge University Press:  12 October 2022

Amrik Singh Nimbran
Amrik Singh Nimbran*
Affiliation:
B3-304, Palm Grove Heights, Ardee City, Sector 52, Gurugram, 122003 Haryana, India e-mail: [email protected]
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Extract

The correspondence between the discrete and the continuous is a fascinating theme in mathematics. The Euler-Maclaurin sum formula, discovered independently and almost contemporaneously by Leonhard Euler (1707–1783) and Colin Maclaurin (1698–1746), in the early 1730s, relates the sum of the values of a function at the integers in the interval [a, b] with its integral over [a, b]. It thus equates a discrete sum with a continuous sum (integral) of a related function.

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 567 , November 2022 , pp. 443 - 457
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Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

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References

Rota, G.-C., Combinatorial snapshots, Math. Intelligencer 21 (1999) pp. 8–14.Google Scholar
Euler, L., Methodvs generalis svmmandi progressiones, Commentarii Academiae Scientiarum Petropolitanae 6 (1738) pp. 68–97.Google Scholar
Euler, L., Methodus vniversalis seriervm convergentivm svmmas qvam proxime inveniendi, Commentarii academiae scientiarum Petropolitanae, 6 (1741) pp. 3–9.Google Scholar
Jacob, W., IV and Osler, T. J., Translation with notes of Leonhard Euler’s Methodvs vniversalis seriervm convergentivm svmmas quam proxime inveniendi, Rowan University. 2006, http://eulerarchive.maa.org/backup/E046.html Google Scholar
Euler, L., Inventio svmmae cvivsqve seriei ex dato termino generali, Commentarii academiae scientiarum Petropolitanae 8, (1741) pp. 9–22.Google Scholar
Euler, L., Methodvs vniversalis series svmmandi vlterivs promota. Commentarii academiae scientiarum Petropolitanae, 8 (1741), pp. 147–158.Google Scholar
Euler, Leonhard, Institutiones calculi differentialis cum eiususu in analysi finitorum ac doctrina serierum, Academiae Impertalis scientiarum Petropolitanae (1755) part II, chapter I.Google Scholar
Maclaurin, C., A treatise of fluxions in two books, T. W. and T. Ruddimans, Edinburgh (1742).Google Scholar
Roy, R., Sources in the development of mathematics: Infinite series and products from the fifteenth to the twenty-first century, Cambridge University Press (2011).CrossRefGoogle Scholar
Tweedie, C., James Stirling: A sketch of his life aud works along with his scientific correspondence, Oxford University Press (1922).Google Scholar
Tweedie, C., Notes on the life and works of Colin Maclaurin. Math. Gaz. 9 (January 1919) pp. 303–305.Google Scholar
Knopp, Konrad, Theory and application of infinite series, Dover, (1990).Google Scholar